Information on Result #878353
Linear OOA(12829, 1048579, F128, 2, 10) (dual of [(1048579, 2), 2097129, 11]-NRT-code), using OOA 2-folding based on linear OA(12829, 2097158, F128, 10) (dual of [2097158, 2097129, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(12829, 2097159, F128, 10) (dual of [2097159, 2097130, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(12829, 1048579, F128, 3, 10) (dual of [(1048579, 3), 3145708, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12829, 1048579, F128, 4, 10) (dual of [(1048579, 4), 4194287, 11]-NRT-code) | [i] | ||
| 3 | Digital (19, 29, 1048579)-net over F128 | [i] | ||